A source moves towards a stationary observer with a speed of 20m/s. If the frequency of the source is 100Hz and speed of sound = 330m/s, determine the apparent frequency heard by observer(ii) Determine the wavelength of sound heard by the observer in part (i)a.104.5Hz; 3.67 mb.106.45Hz; 3.10mc.108.5Hz; 2:10 md.104.5Hz; 3.10 me.108.5Hz; 3.55mf.96.45Hz; 3.55m
Question
A source moves towards a stationary observer with a speed of 20m/s. If the frequency of the source is 100Hz and speed of sound = 330m/s, determine the apparent frequency heard by observer(ii) Determine the wavelength of sound heard by the observer in part (i)a.104.5Hz; 3.67 mb.106.45Hz; 3.10mc.108.5Hz; 2:10 md.104.5Hz; 3.10 me.108.5Hz; 3.55mf.96.45Hz; 3.55m
Solution
The question is asking for the apparent frequency heard by the observer and the wavelength of the sound heard by the observer.
(i) To find the apparent frequency, we can use the Doppler effect formula for sound:
f' = f * (v + vo) / (v - vs)
where: f' is the apparent frequency, f is the source frequency, v is the speed of sound, vo is the speed of the observer, vs is the speed of the source.
Given that the observer is stationary (vo = 0), the source is moving towards the observer (vs = -20 m/s), the speed of sound v = 330 m/s, and the source frequency f = 100 Hz, we can substitute these values into the formula:
f' = 100 * (330 + 0) / (330 - (-20)) = 100 * 330 / 350 = 94.29 Hz
(ii) The wavelength of the sound heard by the observer can be found using the formula:
λ = v / f'
where λ is the wavelength, v is the speed of sound, and f' is the apparent frequency. Substituting the given values:
λ = 330 / 94.29 = 3.50 m
So, the apparent frequency heard by the observer is approximately 94.29 Hz and the wavelength of the sound heard by the observer is approximately 3.50 m. None of the provided options match these results.
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